Abstract:
With applications in scheduling, networks, and generalized assignment problems, integer programs are ubiquitous in a variety of engineering disciplines. Often, integer programming algorithms make use of strategically chosen cutting planes in order to trim the region bounded by the linear constraints without removing any feasible points. Recently, there has been a resurgence of interest in the theory of (minimal) cut generating functions, as such functions can be used to produce quality cuts. Moreover, the family of minimal functions forms a convex set; in order to better understand this class of functions, we wish to study the extreme functions of this set. In this talk, we shall see that the set of continuous minimal cut generating functions contains a dense subset of extreme function.